Power allocation method for MIMO transmit beamforming
A transmit power allocation method for computing a transmit beamforming W matrix for a N streams of data, the method has a first step of measuring a receive channel characteristic H matrix, a second step of decomposing the H matrix into a U matrix which is formed from the left eigenvectors of the H matrix, an Σ matrix which is a diagonal matrix formed from the square roots of the eigenvalues of said H matrix and re-ordered by strength, and a VT matrix with rows comprising the right eigenvectors of H, such that UΣVT=H. The transmit beamforming W matrix is then formed from the re-ordered V matrix of the previous decomposition. Optional waterfilling methods for a plurality of subcarriers may then be done using either a minimum mean square error, an optimal signal to noise ratio, or any other waterfilling method which optimizes a desired metric, such as signal to noise ratio or minimum mean square error.
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The present invention relates to frequency domain beamforming for use in a multiple-input multiple-output (MIMO) wireless system having a plurality of transmit antennas. In particular, the present invention relates to improving channel performance by changing transmit channel subcarrier levels, thereby improving the performance of a remote receiver having one or more receive antennas and associated signal processing paths receiving the signal streams which have been beamformed by the transmitter.
BACKGROUND OF THE INVENTIONBeamforming in MIMO systems is a well known technique that improves the performance of a wireless link using multiple antennas at the transmitter and receiver, and prior knowledge of the channel characteristic. In MIMO systems, the input symbols are mixed across the transmit antennas such that the MIMO channel signal level observed by the receiver is improved. The modulation method Orthogonal Frequency Division Multiplexing (OFDM) simplifies wideband beamforming by separating a frequency selective wideband channel into multiple subcarriers, each subcarrier occupying a narrowband spectrum of the wideband channel. Each subcarrier can be beamformed in the frequency domain using narrowband beamforming techniques known in the prior-art. Beamforming is currently supported by OFDM based IEEE wireless local area network (WLAN) standards such as IEEE WLAN 802.11n and 802.16e.
Y=HWS+N
where:
Y is the receive matrix,
H is the channel characterization matrix,
W is the transmit beamforming matrix,
S is a matrix contains the streams of data to be transmitted, and
N is system noise.
The following equations describe the matrix form of the 2×2 MIMO system of
where:
yk is the received signal at the kth receive path
hik is the channel between the ith transmit antenna and the kth receive antenna
nk is the noise signal at the kth receive path
s1, s2 are the two transmitted symbols
wi, j are the beamforming coefficients and W is the beamforming (mixing) matrix
The value transmitted on each antenna x can be represented as
By computing the values of W using knowledge of the channel characteristic H, it is possible to improve the receive signal quality at the receiver.
OBJECTS OF THE INVENTIONA first object of this invention is the computation of a beamforming matrix W by performing a singular value decomposition of the receive channel characteristic H matrix, the decomposition forming a U matrix which is formed from the left eigenvectors of H, an Z matrix which is a diagonal matrix consisting of the square roots of the eigenvalues of H re-ordered by strength, and a VT matrix with rows comprising the right eigenvectors of H, such that UΣVT=H, whereafter the W matrix used for beamforming is derived from the V matrix.
A second object of the invention is the generation of a beamforming matrix W by performing a singular value decomposition of the receive channel characteristic H matrix, the decomposition forming a U matrix which is formed from the left eigenvectors of H, an Σ matrix which is a diagonal matrix consisting of the square roots of the eigenvalues of H re-ordered by strength, and a VT matrix with rows comprising the right eigenvectors of H, such that UΣVT=H, whereafter the W matrix used for beamforming is derived from the V matrix, and the W matrix is subsequently modified by waterfilling each subcarrier.
SUMMARY OF THE INVENTIONIn a MIMO system supporting N streams of data, a first step is performed whereby a receive channel characteristic matrix H is decomposed into a U matrix which is formed from the left eigenvectors of H, an Σ matrix which is a diagonal matrix consisting of the square roots of the eigenvalues of H ordered by strength where λ1 corresponds to the strongest eigenvalue and λN corresponds to the weakest eigenvalue, and a VT matrix with rows comprising the right eigenvectors of H, such that UΣVT=H. The singular value decomposition operation inherently provides the engenvalues in descending order with stream 1 having the stronger eigenvalue.
In a second step, all the N subcarrier eigenvalues λk,1 of the first stream are sorted across subcarriers (k) in descending order, with the strongest eigenvalues being λ′1,1. The eigenvalues of the second stream are already paired with their corresponding eigenvalues from the first stream. Therefore, as a result of sorting λk,1, if the subcarrier index k of a particular eigenvalue changes, the index of its pair λk,2 also changes. The sorted eigenvalue pairs λ′k,m are then alternately distributed to the two streams. Of the first eigenvalue pair λ′1,1 and λ′1,2, λ′1,1 is assigned to stream 1 and λ′1,2 is assigned to stream 2 and in case of the second eigenvalue pair λ′2,1 and λ′2,2, λ′2,1 is assigned to stream 2 and λ′2,2 is assigned to stream 1. If an eigenvalue λ′k,1 is assigned to one stream the corresponding weaker eigenvalue λ′k,2 of the pair is automatically assigned to the other stream. This has the effect of swapping the eigenvalues across streams for a few subcarriers. This can be achieved by using the V matrix for the beamforming matrix W, by switching the columns of the V matrix.
After the eigenvaues are assigned to alternate streams, the eigenvalues λ′k,m are reassigned to their original subcarrier positions λ″k,m.
In a third step after the eigenvaues are assigned to alternate streams, a waterfilling technique such as minimum mean square error (MMSE) is applied to each stream independently, such that for N=2:
-
- where:
- Φk,m=amplitude of subcarrier k for stream m;
- ν=noise variance;
- μ is the waterfilling limit.
The final beamforming matrix W (for N=2) is given by
The beamforming coefficients of the W matrix can be computed based on an estimate of the transmit channel. This can be obtained from the receive channel estimates based on channel reciprocity:
where H is the receive path channel and H′ is the transmit path channel.
The transmit path channel can also be obtained explicitly from the destination receiver by encapsulating these values in a downstream packet using a variety of methods, including those described in the IEEE 802.11n standard, which provides support for both techniques for estimation of the transmit channel. The computed W beamforming coefficients are then optionally waterfilled by multiplication by a waterfilling matrix, and then applied as W′ coefficients to the transmitted sub carriers.
Computing the singular value decomposition (SVD) of the H matrix for a particular subcarrier may be described as follows:
Where:
U is a 3×3 unitary matrix with columns comprising the left eigenvectors of H,
VT is a 3×3 unitary matrix with rows comprising the right eigenvectors of H,
Σ is a diagonal matrix consisting of the square root of the eigenvalues of H where λ11/2 corresponds to the strongest eigenvalue and λ31/2 corresponds to the weakest eigenvalue.
The left and right eigenvectors are orthogonal to each other (a dot product of any two eigenvectors results in a null) and can be used to decompose the MIMO channel into parallel single input single output (SISO) channels. Each of the three sets for a particular subcarrier frequency is known as an eigenmode, and each eigenmode comprises a left eigenvector, an eigenvalue and a right eigenvector. For example, [h11, h21, h31], λ11/2, [v11, v21, v31] is the first eigenmode.
Step 610 accomplishes the transmission beamforming using the two strongest eigenmodes by selecting the first two columns of the V matrix as the beamforming matrix W.
The resulting channel can be represented as:
Multiplying by UT at the receiver the channel becomes,
Hence the overall channel is decomposed into two independent paths having SNRs of λ1/ν and λ2/{acute over (ν)}, where ν is the noise variance.
Step 616 involves waterfilling across the subcarriers, where waterfilling is a technique used to further enhance the performance of the MIMO wireless link by adding power to certain subcarriers, resulting in the optimal allocation of power to the eigenmodes with the constraint that the total power remains the same.
For a 3×3 MIMO wireless link with two streams, beamforming with waterfilling can be represented as,
Where
Φm2 is the power allocated to the mth eigenmode
and ΣΦm2=1
Hence the beamforming matrix W can be computed as,
One use of waterfilling is to enable a maximum information rate. The waterfilling equation for maximum information rate is given by
Φm2=(μ−ν/λm)+
where:
λm is the mth eigenvalue,
ν is the noise variance,
(.)+ Indicates that the value equals 0 if the expression is negative,
μ is the waterline and is selected based on the power constraint ΣΦm2=1
In order to achieve the maximum information rate, the bit rate for each stream has to be allocated based on its corresponding SNR.
Another application of waterfilling is based on minimum mean square error (MMSE) across streams. The waterfilling equation for minimum mean square error across streams is given by
Φm2=(μ(ν/λm)1/2−ν/λm)
This waterfilling solution is preferred when both the streams are constrained to have equal rates.
Another waterfilling solution is waterfilling across OFDM Subcarriers. The total number of channels in a MIMO OFDM link is N*S where S is the number of spatial streams and N is the number of subcarriers. For optimal power allocation at the transmitter, the waterfilling algorithm should operate over all the available subcarriers as well as the eigenmodes. The MMSE waterfilling solution is this case is given by:
Φk,m2=(μ(ν/λk,m)1/2−ν/λk,m)
ΣΦk,m2=Nsubcarriers
Where the objective is to ensure approximately an equal distribution of signal strengths across the two streams, the flowchart in
The number of iterations required on an average for computing the waterfilling coefficients is significantly reduced compared to prior art waterfilling. For a 2×2 system, the number of iterations to converge within 1 dB of the power constraint could be as high as 12. However, with the eigenvalue spreading shown in
Claims
1. A method for computing a transmit beamforming W matrix for a plurality M streams of data over N subcarriers, the method comprising:
- a first step of measuring a receive channel characteristic H matrix;
- a second step of a transmit beamformer decomposing said H matrix into a U matrix which is formed from the left eigenvectors of said H matrix, an Σ matrix which is a diagonal matrix formed from the square roots of the eigenvalues of said H matrix, and a VT matrix with rows comprising the right eigenvectors of H, such that UΣVT=H;
- where said transmit beamforming W matrix is derived from said V matrix by swapping the strongest column of said V matrix with a different column of said V matrix when a first said eigenvalue associated with said strongest column is greater than a second said eigenvalue corresponding to said different column, said V matrix containing at least two non-zero columns.
2. The method of claim 1 where deriving said W matrix includes waterfilling at least one said subcarrier.
3. The method of claim 1 where deriving said W matrix includes waterfilling each subcarrier using a minimum mean square error for each said subcarrier.
4. The method of claim 3 where said waterfilling using a minimum mean square error comprises computing a power contribution for each k subcarriers and each of m streams according to: ϕ k, m 2 = ( u ( v / λ k, m ) 1 / 2 - v / λ k, m ) ∑ ϕ k, m 2 = N subcarriers
- where Nsubcarriers is equal to said N.
5. The method of claim 1 where said transmit beamforming W matrix is derived from said V matrix by sorting said eigenvalues for each said subcarrier.
6. The method of claim 1 where said second step includes selecting the strongest two eigenvalues for each subcarrier and using the columns of VT associated with said strongest two eigenvalues to form said W matrix.
7. A method for forming a beamforming matrix W from a channel characterization matrix H, each said W and said H having a value for each of N subcarriers, the method having the steps:
- a first step of a transmit beamformer decomposing, for each said subcarrier, said H matrix into a U matrix which is formed from the left eigenvectors of said H matrix, a Σ matrix which is a diagonal matrix formed from the square roots of the eigenvalues of said H matrix, and a VT matrix with rows comprising the right eigenvectors of H, such that UΣVT=H;
- a second step of sorting said eigenvalues in descending order for each said subcarrier;
- a third step of arranging the columns of said VT matrix such that each column associated with a particular eigenvalue is ordered according to the order of said eigenvalues for each said subcarrier;
- a fourth step of arranging the relative strength of each subcarrier using a waterpouring subcarrier equalization method.
8. The method of claim 7 where said waterpouring subcarrier equalization method operates over all eigenmodes and subcarriers.
9. The method of claim 7 where said waterpouring subcarrier equalization method is minimum square error constrained by: ∑ ϕ m 2 = 1.
- Φm2=(μ(ν/λm)1/2−ν/λm)
- where:
- λm is the mth eigenvalue,
- ν is the noise variance,
- μ is the waterline and is selected based on the power constraint
10. A method for forming a beamforming matrix W from a channel characterization matrix H, each said W and said H having a first stream value and a second stream value for each of N subcarriers, the method having the steps:
- a first step of decomposing, for each said subcarrier, said H matrix into a U matrix which is formed from the left eigenvectors of said H matrix, a Σ matrix which is a diagonal matrix formed from the square roots of the eigenvalues of said H matrix and re-ordered by strength, and a VT matrix with rows comprising the right eigenvectors of H, such that UΣVT=H;
- a second step of initializing a first accumulator value to the eigenvalue for a first stream, a second accumulator value to the eigenvalue for a second stream, and a subcarrier iteration variable k to a first value;
- iterate over all said subcarriers using said variable k, where: if said first accumulator value is greater than said second accumulator value, swapping said kth columns associated with a first stream and a second stream of said V matrix; incrementing said k and adding an eigenvalue for a first stream to said first accumulator value, and adding an eigenvalue for a second stream to said second accumulator value;
- thereafter waterfilling each subcarrier W matrix value.
11. The method of claim 10 where deriving said W matrix includes waterfilling each subcarrier using a minimum mean square error for each said subcarrier.
12. The method of claim 10 where said waterfilling using a minimum mean square error comprises computing a power contribution for each k subcarriers and each of m streams according to: ϕ k, m 2 = ( u ( v / λ k, m ) 1 / 2 - v / λ k, m ) ∑ ϕ k, m 2 = N subcarriers
- where Nsubcarriers is equal to said N.
13. The method of claim 10 where said transmit beamforming W matrix is derived from said V matrix by sorting said eigenvalues for each said subcarrier.
14. The method of claim 10 where said second step includes selecting the strongest two eigenvalues and using the columns of VT associated with said strongest two eigenvalues to form said W matrix.
20050094598 | May 5, 2005 | Medvedev et al. |
20060155798 | July 13, 2006 | Ketchum et al. |
20070191066 | August 16, 2007 | Khojastepour et al. |
20070268181 | November 22, 2007 | Howard et al. |
20080080634 | April 3, 2008 | Kotecha et al. |
20080304464 | December 11, 2008 | Borkar et al. |
20080311859 | December 18, 2008 | Ponnampalam et al. |
Type: Grant
Filed: Jun 6, 2008
Date of Patent: Dec 20, 2011
Patent Publication Number: 20090304103
Assignee: Redpine Signals, Inc. (San Jose, CA)
Inventors: Karthik Vaidyanathan (Bangalore), Sailaja Dharani Naga Sankabathula (San Jose, CA)
Primary Examiner: David C. Payne
Assistant Examiner: Syed Haider
Attorney: File-EE-Patents.com
Application Number: 12/134,215
International Classification: H04B 7/02 (20060101); H04L 1/02 (20060101);